Such catalysts, which catalyze the transformation of CO, CO.sub.2 and H.sub.2 to methanol, have been known for some time. At temperatures of 200.degree. to 300.degree. C. and pressures between 30 and 250 bar they give satisfactory yields of methanol, and the length of their useful life is good. In these known catalysts, the atomic ratios between copper and zinc may vary, but generally the copper is present in excess. Furthermore, a part of the zinc component may be partially replaced by calcium, magnesium and/or manganese. The aluminum oxide used as thermostabilizing substance may also be partially replaced by chromium oxide.